Page 92 - ICSE Math 8

Example 4: In a particular type of fertilizer, the ratio of ammonia and potash is 2 : 5. If 2 kg ammonia is
mixed with 14 kg fertilizer, what will be the new ratio of ammonia and potash?
2
Solution: Weight of ammonia in 14 kg fertilizer = (2 + 5) × 14 kg = 4 kg

5
Weight of potash in 14 kg fertilizer = (2 + 5) × 14 kg = 10 kg

4 + 2 6
After adding 2 kg ammonia, the new ratio is 10 = 10 = 3 : 5.

Continued Ratio

Comparison of the magnitude of three or more quantities of the same kind by a ratio is known as continued
ratio. If a, b and c are three quantities such that the ratio of the first two quantities is a : b and the ratio of the
last two quantities is b : c, then the three quantities are in continued proportion and it is denoted by a : b : c.

Example 5: If A : B = 5 : 8 and B : C = 7 : 10, find the continued ratio of A : B : C.
Solution: Make the antecedent of the second ratio equal to the
consequent of the first ratio. Try These
10 80 1. Divide 1,504 g in the ratio 11 : 5.
B : C = 7 : 10 = 1 : = 8 :
7 7 2. If P : Q = 12 : 17 and Q : R = 21 : 26,
find P : R.
So, A : B = 5 : 8 and B : C = 8 : 80
7
80
⇒ A : B : C = 5 : 8 : (Multiplying by the LCM of denominators, i.e., 7)
7
= 35 : 56 : 80
Alternatively,
Make the consequent of the first ratio and the antecedent of the second ratio one and then
combine.
5 10
A : B = 5 : 8 ⇒ A : B = : 1 and B : C = 7 : 10 ⇒ B : C = 1 : 7
8
5 10
⇒ A : B : C = : 1 :
8 7
5 10
= × 56 : 1 × 56 : 7 × 56 (Multiplying by the LCM of denominators, i.e., 56)
8
= 35 : 56 : 80

EXERCISE 8.1

1. Find the ratio between the following (if possible).
(a) ` 273 and ` 117 (b) 480 kg and 210 km (c) 224 balls and 308 balls
2. Find the greater ratio in each of the following.
(a) 6 : 11 and 8 : 13 (b) 16 : 25 and 34 : 59 (c) 14 : 23 and 31 : 46

3. Divide the following.
(a) ` 1,054 in the ratio 11 : 6 (b) 2,808 km in the ratio 23 : 13 (c) ` 2,400 in the ratio 4 : 5 : 11
4. Two numbers are in the ratio 7 : 6. If 2 is subtracted from the first number and 6 from the second number,
then the ratio becomes 4 : 3. Determine the two numbers.

80